At several points we have touched on the definition of states, and you probably have a rather good idea of what I have to say about it now. Still, this is an important issue and it is worth being stated clearly. Besides, we'll get to see (and resolve) a few more “paradoxes,” which should be fun.

CAUSALITY

Newcomb's Paradox

Consider the following “paradox,” attributed to Newcomb and related by Nozick (1969). You are presented with two boxes. One is opaque, and may or may not contain $1M. The other is transparent, and it contains $1,000. You are asked to choose between taking the content of the opaque and of both.

Yes, both, there is no typo here. Indeed, it sounds like a dominant choice to take both. However, there is a twist. In the original version, the person who presents you with the boxes is an omniscient predictor, who can predict your choice with perfect accuracy. Further, she remunerates modesty and penalizes greediness. If she predicted that you'd choose both, she put no money in the opaque box, and vice versa. What is your choice?

Since I find it hard to comprehend what is an omniscient predictor, and how I can know that such a predictor exists while still have a notion of free will, let's change the story a bit.